Among the oldest and most studied topological indices, there are two classical vertex-degree based topological indices–the first Zagreb index and second
Zagreb index. The Zagreb indices were first introduced by Gutman et al. in [1]}, [2]}; they present an important molecular descriptor closely correlated with many chemical properties.
The first Zagreb index \(M_{1}(G)\)  is defined as
\( M_{1}(G)=\sum _{v\in V(G)}\deg (v)^{2}.\) 
